Approval Voting fish (2)

[MIKE OSSIPOFF]

>At 13:19 03.03.00 , Craig Carey wrote:
>:
>:Proof that the 1 winner [Approval] Vote method allows subsequent
>: preferences to act against earlier preferences (invariance on
>: truncation, that test that passes STV). (This example is also a
>: proof that the Alternative Vote fails P2 and P1.)
>:
>:Paper = A>B  (A B .)
>:Candidate:   A   B   C
>:2 Voters:    2   2   0
>:Others:     60  61  62
>:Total:      62  63  62
>:Winner = B
>:
>:Paper = A>B>C  (A B C)
>:Candidate:   A   B   C
>:2 Voters:    2   2   2
>:Others:     60  61  62
>:Total:      62  63  64
>:Winner = C
>:
>:The alteration is this: (AB+)--(ABC+)
>:That is a P2 violation since a change occured when the last preference
>: was filled in, and it is also a P1 violation since [an] alteration
>: was made in (ABC+) at and/or after the preference for B (i.e. the 2nd
>: preference), and B changed from a loser into a winner.
>:
>
>(So "Subsequent can preferences harm candidates supported by earlier
>  preferences, in the Approval Voting  method".)

I freely admit that in Approval when you vote a preference for
your compromise over your favorite, you've cancelled your
preference for your favorite over your compromse. I admit
that Approval isn't pairwise-count, and I point out that
Borda & IRV aren't pairwise-count either, and that they
too don't fully & reliably count every preference that you
express. At least Approval counts every preference that you
_do_ express. That can't be said for Borda or IRV. And
it's easy to make a method protect preferences involving
one's favorite to be cancelled by preferences among lower
choices: Add a rule to eliminate your favorite before counting
your preferences for lower choices. That's how IRV does it.
Saved by being eliminated?

>
>
>...
> >But where you're really inexplicably wrong is where you say that
> >FPTP has no similar problem. ...
>
>"Similar problem" here, means the problem of deciding how many Approval
>  sub-votes to cast. That is a strategic voting problem entirely absent
>  from STV/AV and FPTP/SNTV.

That sounds more like "same method" than "similar problem".
IRV's strategy problem is actually much more complicated than
that of Approval.


>
>...
> >So all you need to know to vote in Approval is which candidate
> >you'd vote for in FPTP. And if you prefer the mathematical strategy,
>
>That is false in general.

Not good enough. Your statement there is unsupported.
If there's a candidate who's a compromise, and is likely to
be the best that you can get, then you vote for him in Plurality.
Vote for him in Approval too. But in Approval you can also
vote for everyone whom you like better.

>
> >it's almost identical with Approval & FPTP, no difference in
> >complexity. (But it's been pointed out that a laborsaving
> >shortcut is possible with Approval, but not with FPTP).
> >
> >But the biggest mis-statement was when you said that single-winner
> >STV has no such problem. If you'd read my uninteresting letter,
>
>It is not clear to me what meaning you have for the word 'problem':
>  either the difficulty of deciding on how many sub-votes to cast
>  or the very similar problem of subsequent preferences disadvantaging
>  earlier preferences. Both those problems are absent from STV &
>  FPTP/SNTV. Perhpas you referred to this paragraph:

I meant strategy dilemma, difficult strategy problems forced
on voters by a voting system. I'm not familiar with the term
sub-votes, but I'm not trying to claim that IRV is the same
method as Approval, only that it has worse strategy dilemma,
due to its failure of defensive strategy criteria, and the
much greater complexity of its strategy.

>
>:* Subsequent preferences harm candidates supported by earlier
>:  preferences, and voters will know that, and then find the decision
>:  (a strategic voting decision) on deciding how many Approval
>:  sub-votes to use, difficult. With FPTP and STV there is no similar
>:  strategic voting problem.
>
>
> >you'd know that I said that single-winner STV has horrendously
> >complicated strategy, and that I've never heard of any mathematician
>
>For the issue of the discourse here, STV is perfect, i.e. perfect in that
>  it requires no strategic voting at all in this matter, because of its
>  property of: subsequent preferences never disadavantaging candidates
>  named by earlier preferences. That is different from "complicated
>  strategy".

I don't call it "perfect" when IRV forces a voter to rank his
2nd choice in 1st place to avoid the election of his last choice.
Condorcet won't do that. Approval won't ever require you to
vote a lower choice over your favorite.

>
> >willing to wade into that problem. When I say "IRV", I'm referring
> >to what you'd call "single-winner STV".
>
>((Why not just follow the British nomenclature?.))

Ok, I'll use "the Alternative Vote". I usually use "IRV", because
the proposals that I'm opposing here, in the U.S., are called
by that name.

>

>
> >>
> >>* The method makes no attempt to keep the power of voters about
> >>   equal. Hence it would be a method not suitable for a land having
> >>   leaders that sought a method that 'fairly summed votes'. It is
> >>   a method that a court could only criticse scathingly.
> >
> >Every voter has the power to vote or not vote for any candidate.
> >All voters equally have that same power. Votes are "fairly summed"
> >if we add up every vote than anyone chooses to give to a candidate.
>
>Maybe instead of "power" in the 1st sentence there you meant freedom.
>The statement "All voters equally have that same power." is false; and
>  I assume power has the commonly understood meaning.

I doubt that it does in voting situations. But I told you what
goal seems to be important to voters, and what strategy problem
is commonly complained about by voters.


> >concerned about. They want to maximize their utility expectation.
>
>That is something that no voter alive wants to do.

Are you suggesting that voters in the United States aren't
alive? :-) Instead of tackling that question, let me just tell
you why I claim voters want to maximize their utility expectation.

I didn't want to do this here, but I'd better talk about the
mathematical strategy of Plurality:

First some preliminary definitions:

Ui is the utility (merit, desirability) of candidate i, as judged
by you. Uj is the utility of candidate j.

Pij is the probability that i & j will be the 2 frontrunners.

The strategic value of candidate i is:

The sum of Pij(Ui-Uj), over all j, where j is is different than i.

To maximize your utility expectation in Plurality, you
should vote for the candidate with the highest strategic value.

I show why that is at the website that I referred you to.

But it's obvious really. The value of voting i over j depends
on how much better i is than j is, and on how likely it is that
they'll be the 2 frontrunners. So vote for the person whose
total value, summed over all the other candidates, is the greatest.

That seems to be just what U.S. voters do. Take the example
with 3 candidates, Worst, Middle, & Favorite.

A voter will tell you that Favorite is much better, better honesty,
better policies, and that Middle & Worst are sleazy & corrupt.
Then he tells you that he's voting for Middle, because the
election will probably be between Middle & Worst. The lesser
likelihood that Favorite will be one of the 2 frontrunners outweighs,
for that voter, the greater merit difference between Favorite
& Worst, as compared to Middle & Worst, and the fact that
Favorite is better than Middle. Let's estimate the strategic
values, as estimated by that voter:

Since Favorite is unlikely to be a frontrunner, then
Pfm & Pfw are quite small. Pmw is large. So much so that
the small value of Um-Uw, when multiplied by the large Pij
isn't so small when compared to Pfw(Uf-Uw), because Pfw is
so small. So when compared to Worst, Middle has a bigger term
than Favorite does, due to Pmw being so much greater than Pfw.

What about their terms with eachother? Um-Uf is negative,
and Uf-Um is positive. But Pfm is so small that the difference
between Pfm(Uf-Um) and Pfm(Um-Uf) is small, and not enough to
offset the relatively huge term that Middle has: Pmw(Um-Uw).

(This shouldn't be taken as a recommendation to vote Democrat.
I'm not saying that that person's utility estimates are accurate).

So that person therefore considers Middle to have highest strategic
value, and votes for Middle, correctly calling that a strategic
vote.

Sure, the voter won't tell you that it's about maximizing
utility expectation by voting for that candidate with highest
strategic value, but that's nevertheless what he's doing, as
best he can estimate.


> >You still haven't named any criteria that Approval fails, and
> >your favorite methods pass. I've named 3 criteria that Approval
> >passes and which Borda & IRV & FPTP fail.
>
>It fails the "truncation resistance" property that STV has. It
>  also a open flop against my P1 and P2 rules.

Truncation resistance is a term for comparing pairwise count
methods. SFC is more generally applicable. Neither Approval nor
IRV nor Borda meets SFC.

One of those two rules that you named requires that preferences
for a lower choice not cancel out a preference for a higher choice
against that lower choice. I told you why claiming that as an
advantage for IRV is fallacious. I'll check on the other P rule
before I comment on it.

I can argue that your criteria for IRV & against Approval aren't
as convincing as my criteria, and I will. But it really comes
down to different people wanting different things from a voting
system. If majority rule & the lesser-of-2-evils problem aren't
important to you, then maybe IRV or Borda will look better to
you. But if you really want something that lives up to the promise
of rank balloting, I suggest Condorcet, in one of the versions
posted on this list.

>
> >>
> >>______________________________________________________________
> >>
> >>At 11:53 02.03.00 , MIKE OSSIPOFF wrote:
>...
> >I told you why Approval is an improvement on Borda. Below in
> >this letter you disagree & I answer.
>
>Missing axioms.
>
>...
> >>Borda has bigger weights for earlier preferences.
> >
> >You missed the point: Why should Borda tell you how many points
> >you can give to candidates. That should be for you to decide.
> >Make that improvement in Borda, and you get something strategically
> >equivalent to Approval. Borda "has weights" for people you might
> >not want to give any votes to. ...
>
>You wrote that "Borda "has weights" for people you might not want to
>  give any votes to. ...". That is referring to the truncation of
>  preference lists. Those weights can be removed by subtracting in a
>  way that leaves the set of winners unchanged.

Those weights can't be removed. Borda, in all the proposals that
I've heard of, requires you to give points to all but one of
the candidates, no matter how much you despise your 2nd to last
choice, and your other lower choices. That doesn't happen with
any other proposed method, and doesn't even happen with FPTP.

Look, maybe Saari was the 1st author you read on voting systems.
One should be skeptical, and not go by the 1st author one runs
across.

>
>Also, the comment "how many points you can give to candidates"
>  indicates a viewpoint problem: if "points" means weights then those
>  weights are data that is internal to the method. That data can be
>  rescaled with altering the method.

If you alter Borda so that it doesn't have that problem, then
its advocates won't accept it. Does Saari accept a version of
Borda that doesn't force you to give votes to all but one
candidate?

>
> >
> >You might say that Approval also doesn't let you decide how many
> >points to give the various candidates you vote for. No, but
> >if you know what you're doing, and want to use your best strategy,
> >you'll give the same point score to all of the ones that you
> >give anything to. In other words, you'll vote as in Approval even
> >if you're free to choose how many points you give to the candidates.
>
>You've assumed constraints but not stated them. This is mathematics:
>  there is no need to hide constraints yet write long paragraphs, or
>  write long messages without describing the constraints' axioms, etc.

If I hid something, that's still hidden from me. Voting in
a flexible system as if it were Approval isn't a constraint; it's
just your best strategy.


>
>
> >>
> >> >
> >> >So, to start improving on Borda, suppose we let you give each
> >> >candidate what _you_ want to give them. That would be a flexible
> >> >point system. It would be a freedom-improvement on Borda.
> >>
> >>The sum of the absolute values of the weights would need to be
> >>  constrained.
> >
> >If the allowed weights must be positive, and you limit how
> >many points you may give, then congratulations, now you have
> >a method that's strategically equivalent to FPTP. A distinct
> >step down from Approval.
>
>This is a greater than anything else you have written, it seems to me.
>You comment would be disagreeable to persons with an STV viewpoint,
>  where preferences soak up some of the vote, and what remains has its
>  power 'transferred to' the next preference.

What I said was only about a point system, and has nothing
to do with STV or its transfers.

>
>I believe that you made many mistakes and I might not reply more.

You have that freedom.


>
>[end]
>
>
Mike Ossipoff
______________________________________________________
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